Answer
Convergent to $0$
Work Step by Step
$a_{n}=\frac{5}{n+2}$
Dividing numerator and denominator by $n$ and evaluating the limit as $n$ tends to infinity, we get
$\lim\limits_{n \to \infty}\frac{\frac{5}{n}}{1+\frac{2}{n}}=\frac{0}{1+0}=0$.
The series converges to zero.
